Now in CND to override customize watch acton for watch node we need to have our own WatchesActionsProvider with all actions (New, Delete, delete all etc.) copy-pasted from core debugger UI. This also requires to have a copy of WatchPanel class. That would be great to have ability to somehow override customize action only.

Well, you can implement NodeActionsProviderFilter. original.getActions() will give you the list of existing actions, which you can override.
Is this sufficient?
The WatchPanel can mostly be replaced by API introduced in issue #181523.

Well, Customize action has no special property to recognize it. But I guess that it will always be the last action in the list. Thus when you're not on a root node, just replace the last action.
I know that this is not 100% reliable, but I do not think this will change in the future...